1.2.5 Discussion of statistical and biological populations

The word population is an important term in both statistics and in biology, and for this reason the term has the potential to cause a lot of confusion if the meaning is not completely obvious from context. The focus of salmon monitoring is almost always groups of fish thought of as members of a biological population. In this sense, a population is a collection of fish whose surviving members will interbreed to sustain the group through time. The population could be subdivided, say into those that are harvested and those that escape the fishery to survive and breed, or the population could be pooled in a larger group linked geographically or by demographic features. Even so, the word population, in this sense remains a collection of animals linked by a relationship—perhaps biological or even administrative.

We often want to describe characteristics of a salmon (biological) population; in some cases we might be able to count and/or measure every fish (i.e., conduct a census).  However, in most cases, this is not feasible.  We need to estimate (or infer) the desired information by sampling part of the biological population.  Statistical sampling and inference requires defining a group of units that represents the biological population.  The entire group of units is called the statistical population.  If we cannot count/measure all the units, we select a sample on which to make the measurements.  Inferences about the statistical population are made based on the sampling design and counts/measurements made on the sample.  The following are some examples of defining statistical populations and their corresponding biological populations:

Suppose you wish to determine the number of sockeye salmon entering a lake.  One way to do that might be to count fish entering the lake with a sonar set to count fish in 15 minute blocks over the period during which fish enter the lake (e.g., between July 15 and Sept. 15.  There are approximately 6,000 15 minute time blocks, making up the statistical population of time blocks.  Fish could be counted in all time blocks (a census), or a sample of time blocks could be counted, then totals determined from the census or estimated from the sample. 

In another example where spawning occurs in a stream network, the statistical population might be defined as a collection of discrete reaches (each reach would be an elementary unit) making up the stream network.  Counting the fish in a sample of reaches would allow estimation of the total number of fish in the network.  In this case the statistical population is discrete (made up of a finite set of identifiable units).  An alternative statistical population could be the continuous stream network (made up of an infinite number of points).  A sample of points could be selected; at each point the number of spawning fish could be counted over a specified distance (e.g., 100 meters).  Then, applying the appropriate inference algorithm, the total number of spawning fish can be estimated.

In some cases, the biological and statistical populations are the same.  Maybe biologists would choose to conduct a mark-recapture study of fish as they enter a lake. In this kind of study a sample of the fish entering the lake would be given some kind of mark. Later, a sample of fish on the spawning ground would be examined for marks, so that the mark rate in the whole population of fish could be measured. With this kind of mark-recapture approach, the statistical population and the biological population would be the same exact collection of fish.

Go Back